a. Field of Invention
The invention relates generally to anatomical modeling. Particularly, the invention relates to a mechanical model of the cardiovascular system for demonstrating physiological principles related to the cardiovascular system including arterial compliance, venous compliance, arterial resistance, the various effects of ventricular filling pressure and filling time on cardiac stroke volume, hypertension and exercise.
b. Background of the Invention and Description of Related Art
The cardiovascular system is basically a pressure driven transport system, moving its constituents macroscopic distances within an organism, coupled to diffusional transport systems that move constituents microscopic distances. The invention focuses on the convective, macroscopic elements of the cardiovascular system. The fluid, blood, is pressurized in the heart and then moves along a pressure gradient to the tissues throughout the body. Blood pressure and blood flow cycle according the cardiac cycle, diastole to systole. Systole is the contraction phase of the cycle in which blood is pressurized and then ejected. Diastole is the relaxation phase in which the ventricle is filled.
Otto Frank, a scientist who contributed greatly to early twentieth century cardiovascular research, was trained in physics and mathematics. His work on ventricular contraction, manometry, and arterial physiology was pivotal to the discipline and his principles were applied in the inventive model. This is discussed in a paper authored by Nichols, W. W. and O'Rourke, M. F. McDonald's Blood Flow in Arteries, London: Arnold, 1998.
Q is a measure of flow, the movement of blood through a given cross-sectional area, and it is referred to as cardiac output (CO). The fundamental purpose of the cardiovascular system is generating and controlling flow, and therefore the purpose of the inventive model is to engineer a model that can generate and control flow.
Darcy, a French engineer, expressed the relationship between pressure, flow, and resistance:
                              Q          ⁡                      (            flow            )                          =                              Δ            ⁢                                                  ⁢            P            ⁢                                                  ⁢                          (              Pressure              )                                            R            ⁢                                                  ⁢                          (              Resistance              )                                                          (                  Eq          .                                          ⁢          1                )            
Poiseuille's law expresses the relationship between flow resistance and the geometry of the vessel. This law applies when flow is laminar in uniform vessels.ΔP/F=R=8ηl/πr4  (Eq. 2)
Where, r=vessel radius, l=vessel length, η=relative viscosity, P=pressure, and R=resistance. Clearly the impact of any change in radius will greatly affect resistance and thereby flow. Levick, Rodney. An Introduction to Cardiovascular Physiology. 4th. New York: Oxford University Press, 2003. Poiseuille's law is utilized in studying peripheral vascular flow but can be inaccurate because of the largely non-Newtonian behavior of blood in the smaller vessels. Vascular resistance is also affected by the arrangement of the resistance vessels. The following equations can account for these relationships:Rtotal=R1+R2+R3 . . . (Series)  (Eq. 3)1/Rtotal=1/R1+1/R2+1/R3 . . . (Parallel).  (Eq. 4)
R1, R2, R3, being resistors in series and the resistance in the aorta, peripheral arteries and arterioles. The sum of resistance in the entire systemic circulation is the Total Peripheral Resistance, Rtotal. Westerhof, Nicolaas. And R. M. Huisman “Arterial haemodynamics of hypertension.” Clinical Science 72 (1987): 391-398.
Blood vessel radius is clearly a crucial regulating factor for total peripheral resistance and thereby blood pressure. Vessel radius is controlled by a number of factors. The local factors include: myogenic response, paracrine factors (NO and metabolites) and physical factors including temperature and pressure. Extrinsic factors also regulate through vasodilator nerves, sympathetic vasoconstrictor nerves, and various endocrine factors.
Compliance and Arterial Resistance: Resistance and compliance are the two primary physical principles controlled by the mammalian cardiovascular system. Compliance can be understood as distensibility. This is discussed in Levick, Rodney, An Introduction to Cardiovascular Physiology. 4th. New York: Oxford University Press, 2003. It is a property of the arterial wall to be distended and then to return to its original shape. During systole, a given volume of blood (stroke volume), moves from the ventricle into the aorta. For all practical purposes, blood is incompressible and this stroke volume must “make room for itself.” It does this by distending the arterial wall and pushing the entire volume of blood further down the peripheral vasculature:
                              Arterial          ⁢                                          ⁢          Compliance          ⁢                                          ⁢                      (            C            )                          =                                            Increase              ⁢                                                          ⁢              in              ⁢                                                          ⁢              Blood              ⁢                                                          ⁢              Volume                                      Increase              ⁢                                                          ⁢              in              ⁢                                                          ⁢              Arterial              ⁢                                                          ⁢              Pressure                                =                                    Δ              ⁢                                                          ⁢              V                                      Δ              ⁢                                                          ⁢              P                                                          (                  Eq          .                                          ⁢          5                )            
Arterial compliance C is a value for the increase in arterial pressure (ΔP) per increase in blood volume in the arterial system (ΔV). This relationship is relatively linear only up to 80 mm Hg, at which point the relationship becomes curvilinear. Arterial compliance is contingent upon a number of factors and is not a constant value. For example, compliance decreases with arteriosclerosis, the stiffening of the arterial vessels. During the cardiac cycle, arterial compliance decreases as the blood pressure rises. This is because of the tensile strength of collagen in the wall. Therefore, an increase in pulse pressure will be the result of an increase in mean arterial pressure. Pulse pressure is defined as the increase in pressure from diastole to systole.
Venous compliance is approximately fifty times greater than arterial compliance. The venous system has a much greater blood capacity and thereby, in humans, a 100 mL blood input will not make much of a difference in the venous pressure. Unlike the arterial system, venous compliance is evident not in the stretching of the vessel walls but rather a change in vessel shape. At low venous pressures, large veins have an ellipsoidal shape and at high venous pressures they have a circular shape. Increased venous blood pressure exerts a stress on the venous walls, causing the vessel to distend and assume a circular form.
Frank Starling Mechanism: The Starling “Law of the Heart” is perhaps the quintessential maxim of cardiac physiology. It states: The greater the stretch of the ventricle in diastole, the greater stroke work achieved in systole. Levick, Rodney, An Introduction to Cardiovascular Physiology. 4th. New York: Oxford University Press, 2003. Stroke work is the stroke volume ejected for given ventricular filling volume. The physiology underlying this law can be divided into two separate aspects, a length-tension relationship and increased contractility. With the length-tension relationship, as the heart muscle is stretched to a greater extent—greater pre-load—there is more optimal overlap between the contractile elements actin and myosin, enabling a greater active contraction force. There also is a degree of passive force from the elastic and tensile elements of ventricular tissue that affect the pressure-volume relationship during ventricular filling. This is provided by the collagen and elastin present in the cardiac tissue. However, the other key component is increased contractility, a muscle length-independent measure of contractile strength. Current literature suggests contractility to be caused by extrinsic control of cardiac activity by systems such as sympathetic nervous activity, as well as increased calcium sensitivity in the cardiac muscle cell. Increased ventricular filling causes an increase in muscle cell stretch. Levick. Enhanced ventricular filling is caused by increased venous pressure. The mechanical model exhibits the change in stroke volume due to increased filling.
Cardiovascular Model Engineering/Modeling the Ventricle: Many mechanical models of the mammalian cardiovascular system have been constructed for the purpose of education and to simulate system behavior. A great challenge to these mechanical systems is the illustration of the “Law of the Heart.” Bag-like ventricles have been utilized for modeling the passively-filling nature of the mammalian ventricle. In this manner, venous pressure can fill the heart and control diastolic volume. The problem that many of these model hearts encounter is that they do not demonstrate appropriate diastolic volumes in relation to arterial pressure. Bayliss (1955) was able to overcome this problem by employing a spring with a cam to assure that contraction occurs quickly and powerfully. Isovolumetric contraction only ends after ventricular pressure is greater than arterial pressure. Bayliss, L. E. “A Mechanical Model of the Heart.” Journal of Physiology 127 (1955): 358-379.
Cardiovascular Model Engineering/Arterial Compliance: The Reverend Stephen Hales (1677-1761) was the first scientist to discover the effects of blood loss on arterial pressure. He also was the first to show that the majority of vascular resistance lies in tiny vessels. Hales describe the arterial system to be similar in function to an “inverted, air-filled dome,” acting to smooth the “pulsatile” nature of blood pressure so that flow would be smooth and constant. It was Hales who described the compression chamber as a windkessel in his book Haemastaticks. Nichols, W. W. and O'Rourke, M. F. McDonald's Blood Flow in Arteries, London: Arnold, 1998
Bayliss' (1955) model featured a capacitance component similar in functioning to that of Westerhof. Bayliss (1955) described this as an “inverted bottle mounted on a side tube just beyond the output valve.” (p. 362) This component is known as a windkessel and it is used in the system to simulate the arterial compliance and venous compliance. Vogel, Steven. Vital Circuits. New York: Oxford University Press, 1992.
The windkessel is a crucial component of the model and some of its previous usages will be discussed. A windkessel is a sealed off container, often a cylinder with a liquid volume beneath an air volume in which liquid moves through the bottom of the windkessel and pressurizes the air above it. An increase in liquid volume decreases air volume and pressurizes the air in the windkessel.
N. Westerhof and R. M. Huisman (1987) constructed a basic, three-component model of the arterial system. Westerhof, Nicolaas. And R. M. Huisman “Arterial haemodynamics of hypertension.” Clinical Science 72 (1987): 391-398. This system consisted of two resistors and a compliance component—a three element windkessel. This model was employed as a load for an isolated cat heart. This system controls the two essential variables of the arterial system: peripheral resistance and arterial compliance. By controlling these two features, pressure and flow behavior could be observed. By using a cat heart, cardiac features such as heart rate, contractility, and filling pressure were controlled and only the two arterial characteristics—compliance and resistance—were changed.
Westerhof et al. (1971) found great success utilizing this three-element model with a windkessel approximation of arterial compliance. Westerhof, Nicolaas, Gijs Elzing a, and Pieter Sipkema. “An artificial system for pumping hearts.” Journal of Applied Physiology 31 (1971): 776-781. They utilized the ideal gas law and the equation for capacitance. Capacitance is a term from electrical engineering for the storage of charge. It is often used in cardiovascular physiology to describe the ability of the veins to store blood volume. In essence, all vessels have a capacitance—an energy storage ability—as they stretch to accommodate a given volume. Pressure energy generated by the heart is stored as potential energy in the tensing of collagen fibers of the vessels. This energy is then released as kinetic energy as the vessels walls recoil, pushing blood down stream. Capacitance can be understood as the physical entity which facilitates the property of compliance. Compliance is the property describing the yielding of a material to a physical force. Westerhof et al. (1971) uses the term capacitance rather than compliance in their description of their mechanical model. They constructed a windkessel to provide a capacitance for the purpose of imitating arterial compliance. In this paper, the term compliance will be used rather than capacitance.PV=RT,  (Eq. 6)C=dV/dP,  (Eq. 7)
Where C=capacitance (compliance); P=pressure, V=volume; T=(absolute) temperature, and R=gas constant. Westerhof et al (1971) thereby utilized the relationship C=V/P in compliance calculations. In situations with constant pressure, a decrease in the volume available for air above the blood volume causes a decrease in compliance. This pivotal relationship served as the foundation for the construction of arterial and venous windkessels in my model.
The model constructed by Westerhof et al. (1971) was superior in capacitance to those employing elastic tubes to simulate compliance because the air reservoir had the ability to be changed and controlled. By utilizing a simple air reservoir above a water volume as in the windkessel, a given capacitance value can be easily reproduced. The arterial model constructed by Westerhof et al. (1971) effectively simulates cardiac load. Westerhof et al. (1971) featured a windkessel design in which air volumes are calibrated and were used as a measure of arterial capacitance. They found that the flow and pressure of their arterial model related well with measurements from in vivo studies. In the study, the non-Newtonian aspects of fluid flow are disregarded.
Cardiovascular Model Engineering/Arterial Resistance: In Bayliss' (1955) classic model, the primary source of resistance in the arterial system is simulated by a screw clamp resistor located prior to the capillary component. In Bayliss' model, changing peripheral resistance did not change venous pressure. When peripheral resistance increased, the hydraulic power of the pump remained the same. Therefore the arterial system increased in fluid capacity, which is stored in the windkessel due to simulated compliance. Nichols noted that this event caused a slight decrease in venous volume in Bayliss' system. For the resistance component, Westerhof et al. (1971) constructed an arterial system that included a block with thousands of narrow flow channels. The side of the block was fixed with an apparatus so that a slide could move down and up to control resistance by closing or opening flow channels.
Modeling Pathology of the Cardiovascular System:
The focus of more recent modeling of the arterial systems is to demonstrate hypertension. Hypertension, chronically high blood pressure, causes a series of pathologic long-term effects. This pathology is also one focus of the invention. The two primary problems of hypertension are the increase in peripheral resistance and the decrease in arterial distensibility. Nichols identified that in hypertension, cardiac output (CO) remains high; therefore, there is an increase in mean arterial pressure. The two primary variables an arterial system can control are arterial compliance and peripheral resistance.